package euler.p001_050;

import java.util.HashMap;
import java.util.Map;
import java.util.Stack;

import euler.MainEuler;

public class Euler014 extends MainEuler {

    /*
        The following iterative sequence is defined
        for the set of positive integers:

        n → n/2 (n is even)
        n → 3n + 1 (n is odd)

        Using the rule above and starting with 13,
        we generate the following sequence:
        13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

        It can be seen that this sequence (starting at 13
        and finishing at 1) contains 10 terms. Although it
        has not been proved yet (Collatz Problem),
        it is thought that all starting numbers finish at 1.

        Which starting number, under one million,
        produces the longest chain?

        NOTE: Once the chain starts the terms are
        allowed to go above one million.
     */

    public String resolve() {

        int limite = 1000000;

        int n = 0;
        int max = 0;

        for (int i = 1; i<limite; i++) {
            int c = getChainLength(i);
            if (c > max) {
                n = i;
                max = c;
            }
        }

        return String.valueOf(n);
    }

    private static final Map<Long, Integer> cl = new HashMap<Long, Integer>();
    static {
        cl.put(1l,1);
    }
    private int getChainLength(long i) {

        if (!cl.containsKey(i)) {

            Stack<Long> s = new Stack<Long>();

            while (!cl.containsKey(i)) {
                s.push(i);
                i = sequence(i);
            }

            while (!s.isEmpty()) {
                i = s.pop();
                cl.put(i,1+cl.get(sequence(i)));
            }
        }

        return cl.get(i);
    }

    private long sequence(long i) {
        return (i % 2 == 0) ? (i/2) : (3*i +1);
    }

}
